Consider the following relation:

Question

{(1, 5), (3, 8), (3, 3), (6, 9), (7, 7)}

Part B) Does this relation pass the vertical line test? How do you know, explain your answer.

Part C) Which ordered pair could be removed so that the relation is a function? Explain your answer.

Answer 1

Part B) A relation passes the vertical line test if there are no two points in the relation that have the same x-coordinate but different y-coordinates.

In this case, the relation {(1, 5), (3, 8), (3, 3), (6, 9), (7, 7)} does not pass the vertical line test because there are two points with the same x-coordinate of 3 but different y-coordinates of 8 and 3.

Part C) To make the relation a function, we need to remove one of the points with the same x-coordinate but different y-coordinates. In this case, we can remove either (3, 8) or (3, 3) since they have the same x-coordinate of 3. Removing either of these points will leave us with a relation that passes the vertical line test and becomes a function.